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# Polynomials intro

Polynomials Intro
Published on: Mar 4, 2016
Published in: Education
Source: www.slideshare.net

#### Transcripts - Polynomials intro

• 1. Block 2 Polynomials Introduction
• 2. What is to be learned? • What a poLynomial is • How you know what degree a poLynomial is • What the big L is, and how it works
• 3. Spot The PoLynomial x2 + 4x – 2 7x + 2 sinx 5x2 -6x7 8x      degree 2 degree 7 degree 1
• 4. A Calculation f(x) = 3x4 – 2x3 + x2 – 4x + 7 f(2)? = 3(2)4 – 2(2)3 + 22 – 4(2) + 7 = 35 Causes a lot of tension
• 5. Introducing the Big L f(x) = 3x4 – 2x3 + x2 – 4x + 7 f(2)? 3 -2 1 -4 7
• 6. Introducing the Big L f(x) = 3x4 – 2x3 + x2 – 4x + 7 f(2)? 3 -2 1 -4 72 3 X 2 6 + 4 X 2 8 + 9 X 2 18 + 14 X 2 28 + 35
• 7. Introducing the Big L f(x) = 3x4 – 2x3 + x2 – 4x + 7 f(2)? 3 -2 1 -4 72 3 X 2 6 + X 2 8 + X 2 18 + X 2 28 + 353 f(2) = 35 4 9 14
• 8. Introducing the Big L f(x) = 4x4 – 5x3 + 2x2 – 3x + 11 f(3)? -5 2 -3 113 4 12 7 21 23 69 66 198 2094 f(3) = 209
• 9. PoLynomials • Expressions with (non negative) powers of x • Highest power gives the • PoLynomial calculations invariably involve The Big L (also known as nested calculation scheme) (by those with a sad lack of imagination) degree
• 10. Calculating Function Values With The Big L f(2)? f(x) = 3x4 – 4x3 + x2 – 2x + 9 3 -4 1 -2 92 X 2 6 + 2 X 2 4 + 5 X 2 10 + 8 X 2 16 + 253 f(2) = 25
• 11. Key Question f(x) = 2x4 – 6x3 + 5x2 – 4x + 16 f(3)? -6 5 -4 163 2 6 0 0 5 15 11 33 492 f(3) = 49
• 12. Beware 3x4 + 2x2 – 7x + 9 3 2 -7 9 no x3 term 0